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A unifrom circular disc of radius 50 cm ...

A unifrom circular disc of radius `50 cm` at rest is free to turn about an axis, which is perependicular to the plane and passes through its centre. It is subjected to a torque which produces a constant angualr acceleration of `2.0 rad//s^(2)`. Its net acceleration in `m//s^(2)` at the end of `2.0 s` is approximately

A

`7.0`

B

`6.0`

C

`3.0`

D

`8.0`

Text Solution

Verified by Experts

The correct Answer is:
D
`r = 50 cm = (1)/(2)m, alpha = 2.0 rad//s^(2)`
`t =2.0 s, a = ?`
Angular speed, `omega = alpha t = 2.0 xx 2.0 = 4 rad//s`
Centripetal acceleration, `a_(c) = omega^(2) r = 4^(2) xx 0.5`
`= 8 m//s^(2)`
Linear/tangential acceleration at the end of `2s`
`a_(t) = alpha r = 2.0 xx 0.5 = 1 m//s^(2)`
`:.` Net acceleration at the end of `2` second
`a = sqrt(a_(c)^(2) + a_(t)^(2))`
`a = sqrt(8^(2) +1^(2)) = sqrt(65) = 8m//s^(2)`
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